Home
Class 12
MATHS
If f(y)=e^(y),g(y)=y,ygt0 and F(t)=int(0...

If `f(y)=e^(y),g(y)=y,ygt0` and `F(t)=int_(0)^(1)f(t-y)g(y)dt` then

A

`F(t)=te^(-t)`

B

`F(t)=1-e^(-t)(t+1)`

C

`F(t)=e^(t)-(1+t)`

D

`F(t)=te^(t)`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test 2|56 Videos

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|143 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|87 Videos

  • DERIVATIVE AS A RATE MEASURER

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|26 Videos

Similar Questions

Explore conceptually related problems

If f(y)=e^y,g(y)=y,y>0, and F(t)=int_0^t f(t-y)g(y) dy , then

If f(y)=e^y ,g(y) = y>0,a n d \ F(t)=int_0^t f(t-y)g(y)dy ,then

If int_(0)^(x)f(t)dt = x^(2)-int_(0)^(x^(2))(f(t))/(t)dt then find f(1) .

If int_(0)^(x)f(t)dt=e^(x)-ae^(2x)int_(0)^(1)f(t)e^(-t)dt , then

If f(x-y)=f(x).g(y)-f(y).g(x) and g(x-y)=g(x).g(y)+f(x).f(y) for all x in R . If right handed derivative at x=0 exists for f(x) find the derivative of g(x) at x =0

If f(x-y)=f(x).g(y)-f(y).g(x) and g(x-y)=g(x).g(y)+f(x).f(y) for all x in R . If right handed derivative at x=0 exists for f(x) find the derivative of g(x) at x =0

Suppose f(x) and g(x) are two continuous functions defined for 0<=x<=1 .Given, f(x)=int_0^1 e^(x+1) .f(t) dt and g(x)=int_0^1 e^(x+1) *g(t) dt+x The value of f( 1) equals

IF f(x+f(y))=f(x)+y AA x, y in R and f(0)=1 , then int_(0)^(10)f(10-x)dx is equal to

Given a function 'g' continous everywhere such that int _(0) ^(1) g (t ) dt =2 and g (1)=5. If f (x ) =1/2 int _(0) ^(x) (x-t) ^(2)g (t)dt, then the vlaue of f'''(1)-f''(1) is:

Given a function 'g' continous everywhere such that int _(0) ^(1) g (t ) dt =2 and g (1)=5. If f (x ) =1/2 int _(0) ^(x) (x-t) ^(2)g (t)dt, then the vlaue of f''(1)-f'(1) is:

OBJECTIVE RD SHARMA ENGLISH-DEFINITE INTEGRALS-Chapter Test 1
  1. The smallest interval [a,b] such that int0^(1) (1)/(sqrt(1+x^(4)))dx...

    Text Solution

    |

  2. Let I(n)=int(0)^(pi//2) sin^(n)x dx, nin N. Then

    Text Solution

    |

  3. If f(x)=int(0)^(x) sin^(4)t dt, then f(x+2pi) is equal to

    Text Solution

    |

  4. int(0)^(pi)(dx)/(1+3^(cos x)) is equal to:

    Text Solution

    |

  5. Let int(0)^(a)f(x)dx = lambda and int(0)^(a)f(2a-x)dx=mu. Then int(0)^...

    Text Solution

    |

  6. Evaluate : int((pi)/(4))^((3pi)/(4))(x)/(1+sinx)dx

    Text Solution

    |

  7. Let I(n)=int(0)^(pi//2) cos^(n)x cos nx dx. Then, I(n):I(n+1) is equal...

    Text Solution

    |

  8. The value of int(-1)^(1) max[2-x,2,1+x] dx is

    Text Solution

    |

  9. int(0)^(pi//4) sin(x-[x]) dx is equalto

    Text Solution

    |

  10. The value of the integral int(-1)^(1) (x-[2x])dx,is

    Text Solution

    |

  11. Let f:R in R be a continuous function such that f(1)=2. If lim(x to 1)...

    Text Solution

    |

  12. Let f:R in R be a continuous function such that f(x) is not identicall...

    Text Solution

    |

  13. Let f(x)=int(0)^(x) |xx-2|dx, ge 0. Then, f'(x) is

    Text Solution

    |

  14. Lt(nrarroo) {(n!)/(kn)^n}^(1/n), k!=0, is equal to (A) k/e (B) e/k (C)...

    Text Solution

    |

  15. int(0)^(sqrt(2)) [x^(2)]dx, is

    Text Solution

    |

  16. Let f(x) be a function satisfying f'(x)=f(x), f(0)=1 and g be a functi...

    Text Solution

    |

  17. (sum(n=1)^10int(-2n-1)^(-2n)sin^(27)(x)dx+sum(n=1)^10int(2n)^(2n+1)sin...

    Text Solution

    |

  18. If f(y)=e^(y),g(y)=y,ygt0 and F(t)=int(0)^(1)f(t-y)g(y)dt then

    Text Solution

    |

  19. If I(n)=int(0)^(pi//2) x^(n) sin x dx, then I(4)+12I(2) is equal to\

    Text Solution

    |

  20. int(0)^(1) sin{2 tan^(-1)sqrt((1+x)/(1-x))}dx=

    Text Solution

    |